1. 385L37

2. Ptolemaic Contributions
• consolidation of earlier models/theories • extension and refinement of Hipparchan trigonometrics • refinement of armillary sphere • data-driven expansion of model • epi-epicycles • mobile eccentricity • equant orbit

3. Armillary Sphere
• Eratosthenes credited with invention; developments by Hipparchus and Ptolemy • geocentric model • rings represent equator, ecliptic, celestial latitudes and longitudes • plots solar and stellar positions and angles • observational instrumentation

4. Retrogression
• exact speed of retrogression varies over time • length of retrograde loops varies : shorter (fast) vs. longer (slow)

5. Epicycle & Eccentric
• epicycle predicts only uniform retrograde loops • eccentric predicts regular changes in angular velocity • eccentric + epicycle predicts irregular seasonal lengths • neither predicts both position and speed of retrogression

6. Ptolemaic Modifications
• re-arrangement of existing models: epi-epicycles • new combinations of models : mobile eccentrics • equant orbits

7. epi-epicycle (Ptolemy)

8. Mobile Eccentric (Ptolemy)
planet (P) on epicycle orbiting point (C) on deferent point (C) orbiting point (G) on epicycle point (G) orbiting eccentric point (F), where E = Earth

9. equant (Ptolemy)

10. Uniform, Eccentric, Equant Orbits

11. Eccentric, Equant, Retrogression

12. BODY
EUDOXOS
KALLIPPOS
ARISTOTLE
PTOLEMY
Moon 3 5
Sun 6
Planets 20 23 44
68+
Stars 1
TOTAL 27 34 56
80+

13. Astronomical Premises
1 sphericity of universe and all celestial objects 2 circularity of all celestial motion 3 perpetual nature of all celestial motion 4 uniformity of all celestial motion 5 uniformity of celestial position/place 6 geocentricity 7 stationary Earth 8 rotation of celestial sphere

14. • Eudoxan spheres consistent with all premises • epicyclic model violates uniform place (5) premise • eccentric and equant models violate circular (2) and geocentric (6) premises

15. Ptolemaic Universe

16. Ptolemaic Contributions
• consolidation of previous models • rigorous mathematization, esp. measurement of angular velocities • enhanced predictability of celestial events (star tables, ephemerides, navigational charts) • reduction (NOT elimination) of some contrary observational data, creation of new contradictories • triumph as mathematical model of universe, failure as astronomical model • skewing of physical astronomy (Aristotle) and mathematical/technical astronomy (Ptolemy)

17. Mathêmatikê Syntaxis
[Mathematical Compilation]
(ca. 150 CE)  Megistê Syntaxis
[Greatest Compilation]  Arabic
Al-magest [The Greatest {Book}]
(9th century)  Latin Almagest
(12th century)  Copernicus
( )